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Simplifying a2 = 24 + -10a Solving a2 = 24 + -10a Solving for variable 'a'. Reorder the terms: -24 + 10a + a2 = 24 + -10a + -24 + 10a Reorder the terms: -24 + 10a + a2 = 24 + -24 + -10a + 10a Combine like terms: 24 + -24 = 0 -24 + 10a + a2 = 0 + -10a + 10a -24 + 10a + a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -24 + 10a + a2 = 0 Factor a trinomial. (-12 + -1a)(2 + -1a) = 0Subproblem 1
Set the factor '(-12 + -1a)' equal to zero and attempt to solve: Simplifying -12 + -1a = 0 Solving -12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1a = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1a = 0 + 12 -1a = 0 + 12 Combine like terms: 0 + 12 = 12 -1a = 12 Divide each side by '-1'. a = -12 Simplifying a = -12Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-12, 2}
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